DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loops

• Published in: IEEE control systems letters Vol. 7; p. 1
• Main Authors: Everett, Michael, Bunel, Rudy, Omidshafiei, Shayegan
• Format: Journal Article
• Language: English
• Published: IEEE 01.01.2023
• Subjects: Aerospace electronics; Artificial neural networks; Collision avoidance; Control systems; Data-Driven Control; Heuristic algorithms; Neural Networks; Reachability analysis; Safety; Safety Verification
• ISSN: 2475-1456; 2475-1456
• DOI: 10.1109/LCSYS.2023.3260731

Safety certification of data-driven control techniques remains a major open problem. This work investigates backward reachability as a framework for providing collision avoidance guarantees for systems controlled by neural network (NN) policies. Because NNs are typically not invertible, existing methods conservatively assume a domain over which to relax the NN, which causes loose over-approximations of the set of states that could lead the system into the obstacle (i.e., backprojection (BP) sets). To address this issue, we introduce DRIP, an algorithm with a refinement loop on the relaxation domain, which substantially tightens the BP set bounds. Furthermore, we introduce a formulation that enables directly obtaining closed-form representations of polytopes to bound the BP sets tighter than prior work, which required solving linear programs and using hyper-rectangles. Furthermore, this work extends the NN relaxation algorithm to handle polytope domains, which further tightens the bounds on BP sets. DRIP is demonstrated in numerical experiments on control systems, including a ground robot controlled by a learned NN obstacle avoidance policy.